Probability that number will include at least 1 seven is [tex]0.3439[/tex] .
Step-by-step explanation:
Here we have , if i were to randomly generate a 4-digit number, We need to find how likely is it that my number will include at least 1 seven . Let's find out:
Out of 10 digits ( 0,1,2,3,4,5,6,7,8,9) , We are supposed to find probability to generate a 4 digit number with at least one times 7 . We can find this as Probability for at least one 7 = 1 - Probability for no 7
Total number of combinations = [tex]10^4[/tex]
Total number of combinations without 7 = [tex]9^4[/tex]
Probability of Number without 7 = [tex]\frac{9^4}{10^4}[/tex]
⇒ Probability of Number without 7 = [tex]\frac{6561}{10000}[/tex]
⇒ Probability of Number without 7 = [tex]0.6561[/tex]
∴ Probability for at least one 7 = 1 - Probability for no 7
⇒ [tex]1-0.6561[/tex]
⇒ [tex]0.3439[/tex]
Therefore ,Probability that number will include at least 1 seven is [tex]0.3439[/tex] .
